Pre-Equilibrium Reaction Mechanism as a Strategy to Enhance Rate and Lower Overpotential in Electrocatalysis

Pre-equilibrium reaction kinetics enable the overall rate of a catalytic reaction to be orders of magnitude faster than the rate-determining step. Herein, we demonstrate how pre-equilibrium kinetics can be applied to breaking the linear free-energy relationship (LFER) for electrocatalysis, leading to rate enhancement 5 orders of magnitude and lowering of overpotential to approximately thermoneutral. This approach is applied to pre-equilibrium formation of a metal-hydride intermediate to achieve fast formate formation rates from CO2 reduction without loss of selectivity (i.e., H2 evolution). Fast pre-equilibrium metal-hydride formation, at 108 M–1 s–1, boosts the CO2 electroreduction to formate rate up to 296 s–1. Compared with molecular catalysts that have similar overpotential, this rate is enhanced by 5 orders of magnitude. As an alternative comparison, overpotential is lowered by ∼50 mV compared to catalysts with a similar rate. The principles elucidated here to obtain pre-equilibrium reaction kinetics via catalyst design are general. Design and development that builds on these principles should be possible in both molecular homogeneous and heterogeneous electrocatalysis.


■ INTRODUCTION
Metal-hydrides are key intermediates in a broad scope of chemistries including solar fuels and organic transformations for commodity and fine chemical synthesis. However, electrocatalytic approaches involving metal-hydride intermediates are universally plagued by a competition between desired product formation (hydride transfer to substrate), and competitive reaction of the hydride intermediate with the protons that are needed in solution to generate the hydride intermediate [via electron-transfer (ET) and proton-transfer (PT) steps, Scheme 1].
An example situation where these competing reactions have been studied is in C−H bond formation with CO 2 and the interest in that chemistry derives from its potential applications in solar fuel chemistry. 1−8 Desired products include formate, methanol, ethanol, or ethylene which all contain C−H bonds; but H 2 formation is an ongoing challenge. Contributions from a number of research groups have demonstrated that we can use catalyst design for thermochemical control of reaction chemistry to achieve selectivity for C−H bond formation over H 2 evolution. 9−16 However, that approach does not necessarily produce fast rates for C−H bond formation with CO 2 . 17 Approaches to enhancing the reaction rate for C−H bond formation with CO 2 are needed, and have primarily used reaction conditions, rather than catalyst design to achieve improvements: successful examples of this approach include stabilization of transition states for hydride transfer to CO 2 by choice of the solvent, 18−25 use of hydride-transfer mediators, 26 or additions of base or alcohol. 27,28 We have previously demonstrated that the large metal carbonyl clusters promote hydride formation with rate 10 8 M −1 s −1 . 29−31 We believe that this fast rate has two possible origins. The multiple metal−metal bonds in the clusters serve as multiple sites for protonation, and this should provide a kinetic boost to the rate of cluster-hydride formation. 30,31 In addition, the high anionic charges, 3− or 4−, on the clusters promote PT: while the delocalized structures of the clusters enable access to modest reduction potentials relative to single-metal site electrocatalysts, at a given formal oxidation state or overall charge. 32 A remaining challenge is to design a complete catalytic cycle competent for solar fuel chemistry or chemical synthesis which has fast hydride formation without H 2 production. Preequilibrium kinetic schemes have been reported as a tool for optimizing rates in O 2 reduction, 33 in hydride formation chemistries, 34 and in CO 2 reduction to CO. 35 Pre-equilibrium dynamics of intermediate formation in a catalytic cycle often impact a subsequent rate. As an example, PT transfer rates to two-electron reduced [CoCp(dxpe)(NCCH 3 )] 2+ complexes [Cp = cyclopentadienyl, dxpe = 1,2-bis(di(aryl/alkyl)phosphino)ethane] can be controlled by the equilibrium constant for dissociation of MeCN from Co prior to PT, 34 and pre-equilibrium kinetics of CO 2 binding to iron(0) porphyrin enhance the observed apparent rate constant for CO formation, under reaction conditions where the thermodynamics for C−O bond-breaking are favorable. 35 Fast H 2 evolution by iron porphyrin also proceeds with a pre-equilibrium kinetic scheme involving fast Fe-hydride formation. 36,37 When conceiving of the work reported herein, we reasoned that fast formation of (H-1) 3− at significant concentrations will boost the formate formation rate by orders of magnitude if (H-1) 3− is formed with very fast rate to enable a pre-equilibrium reaction mechanism. According to the pre-equilibrium approximation, which can be used in the case of a fast initial chemical step in a catalytic cycle, the observed rate of a possible formate formation reaction should scale with the equilibrium constant (K 1 ) for pre-equilibrium hydride formation (Scheme 2), according to eq 1 where k obs (s −1 ) is the observed rate of reaction, K 1 is the equilibrium constant for formation of (H-1) 3− , k 2 (M −1 s −1 ) is the rate for hydride transfer to CO 2 , and [CO 2 ] (M) is the concentration of CO 2 . We further noted during this experimental design that the fast pre-equilibrium chemical step should offer a kinetically derived lowering of the overpotential for the reaction because a fast chemical step following ET results in the anodic shift of the reduction peak potential of any electrocatalyst. Herein, we demonstrate that formate is generated at an overpotential of 10 mV and with the rate of 1.2 × 10 3 M −1 s −1 using 1 3− in 0.1 M Bu 4 NBF 4 MeCN/H 2 O (95:5) (Calculation S1). We can also use stronger acids than water to enhance K 1 , and with anisidinium tetrafluoro borate, it is generated at an overpotential of 64 mV with the rate of 5.07 × 10 2 M −1 s −1 .
The well-understood mechanistic origin of this result from the pre-equilibrium mechanism provides a roadmap for future catalyst design. In principle, any electrocatalytic reaction can be designed with a view to achieving pre-equilibrium intermediate formation to overcome slow rates that might be associated with thermochemically controlled rates for selectivity in subsequent chemical steps using heterogeneous or homogeneous electrocatalysis.

■ RESULTS AND DISCUSSION
To study catalysis by 1 3− , we prepared samples of (PhCH 2 NMe 3 ) 2 [Co 11 C 2 (CO) 23 ] (1 2− ) following a previously published method (PhCH 2 NMe 3 + = benzyl ammonium cation). 38  showed a further increase in j p at −1.054 V, relative to the CV collected under 1 atm N 2 , and this suggests that a catalytic reaction has occurred where hydride is transferred to CO 2 to afford formate (Figure 1 left). Current enhancements consistent with catalytic formate formation were also observed using anisidinium tetrafluoroborate (AnsdH + ) as the source of H + (Figure 1 right).
The most acidic proton source in solutions of CO 2 -saturated 0.1 M Bu 4 NBF 4 MeCN/H 2 O (95:5) is carbonic acid produced from 0.24 M CO 2 in MeCN/H 2 O and that has pK a = 17.03. 39,40 The pK a of AnsdH + in MeCN is 11.86. 41 The waveforms obtained with MeCN/H 2 O (95:5) or with AnsdH + are different. Catalysis with water is observed at similar potential as the reduction potential for 1 3−/4− , whereas catalysis using AnsdH + as the proton source is observed at a potential more anodic than the reduction of 1 3− . A possible mechanistic origin of these waveforms is discussed later, along with the determination of k obs .
Characterization of Formate. Controlled potential electrolysis (CPE) experiments carried out under both 1 atm N 2 and 1 atm CO 2 were performed to identify the product in the CV experiments. CPE experiments −1.13 V over 40 min were followed by analysis of the head space using gas chromatography with thermal conductivity detector (GC-TCD) and analysis of the solution using proton NMR spectroscopy. Using 5% H 2 O as the proton source in MeCN solutions, we determined that the Faradaic efficiency (FE) for formate and H 2 production are 75(5) and 15(2) %, respectively (Table S1, Figures S2−S4, see the Supporting Information for experimental details). CPE experiments performed using AnsdH + as the source of protons under 1 atm CO 2 were run at −0.9 V, and those yielded formate and H 2 with FE of 70(8) and 25(3)%, respectively (Table S1, Figures S2 and S3). No CO 2 -reduced products were detected by proton NMR when the CPE experiments were carried out under 1 atm N 2 or in the absence of 1 2− under 1 atm CO 2 . To confirm the carbon source, isotopically labelled 13 CO 2 was used for CPE experiments, and the 13 C{ 1 H} NMR spectrum collected of the CPE solution showed a peak at 172.9 ppm which conclusively indicates that formate was produced from CO 2 during electrocatalysis ( Figure S3D). CPE experiments run with the used electrodes from CPE experiments containing 1 2− , and those also produced no carbon-containing products. SEM−EDX measurements performed on used electrodes revealed no deposited Co on the glassy carbon ( Figure S5).
Mechanistic Studies of Hydride Formation. Our first step toward understanding the mechanism for formate formation by 1 3− was to measure the rate for catalyst-hydride, (H-1) 3 Figure 2). Under N 2 , the reductive peak potential E p,c shifted from E 1/2 anodically by 100 mV relative to CVs lacking H 2 O, which suggests a fast rate for PT following the ET. The 1 3−/4− redox couple is also observed at a consistent potential in these CVs, which suggests that some of the 1 2− is regenerated from (H-1) 3− in a reaction with protons during the CV experiment, and some of the (H-1) 3− remains and is oxidized at −0.72 V on the return scan.
For a chemical reaction that proceeds ET, the peak potentials (E p ) shift anodically relative to the formal potential of 1 3−/4− (E 1/2 ). The kinetic information is contained in the "peak shift", ΔE p (where ΔE p = E p − E 1/2 ) according to 2 42,43 , k 1 is the second-order rate constant of the PT reaction (s −1 ), and other symbols were defined earlier. Due to the fast catalysis following the formation of (H-1) 3− (vide infra), eq 2 is potentially a little inaccurate in this situation, and therefore, we also determined a value for k 1 using a foot-of-the wave analysis (FOWA), 44,45 so that the two measurements can be compared. Experimentally, k 1 can be obtained by recording E p − E 1/2 as a function of υ, and we performed this experiment with a ratio of [H + ]/[1 2− ] = 3800, where E p − E 1/2 is already ∼150 mV due to the fast PT step. A plot of (E p − E 1/2 )F/RT vs ln(υ) according to eq 2 gave k 1 = 3.9 × 10 5 M −1 s −1 under 1 atm N 2 (Table 1, Figure 2 left, Calculation S2). The same experiment was repeated under 1 atm CO 2 , and a higher rate of 1.2 × 10 7 M −1 s −1 was observed for k 1 (Table 1, Figure 2 right, Calculation S2). This higher rate for k 1 is consistent with carbonic acid as the proton source, which has lower pK a than H 2 O as the proton source in MeCN. The value of k 1 measured using AnsdH + as the proton source was the same (within error) under 1 atm of N 2 or CO 2 and is 3 × 10 8 M −1 s −1 (  Figure S7).
Catalytic Formate Formation Rate and Mechanism. Our next effort toward understanding the effects of pre-   Figure S8). The rate of formate formation by 1 2− (k obs , s −1 ) can be obtained using a fast scan CV measurement of the limiting current (i lim ). 46,47 The experiment is performed with excess substrate relative to the catalyst to achieve i lim , which is independent of the scan rate due to mutual compensation of substrate depletion during catalysis and diffusion. These reaction conditions also lead to the form of eq 1, where neither [1 3− ] or [H + ] influences k obs . Analysis of i lim to measure the rate of formate formation under 1 atm CO 2 was performed using the same two sources of protons as mentioned above: CO 2 -saturated H 2 O and AnsdH + , in 0.1 M Bu 4 NBF 4 MeCN solution (Calculation S4, Figure 4). In addition, the k obs values obtained were corrected for the measured FE which are 75 and 70% for formate under 1 atm CO 2 , in MeCN/H 2 O (95:5) and MeCN with added AnsdH + , respectively. Therefore, the values for k obs are 296 and 142 s −1 , respectively, in MeCN/H 2 O (95:5) and MeCN with added AnsdH + , under 1 atm CO 2 ( Table 1).
A comparison of the data collected with low [H + ] ( Figure 2) and with high [H + ] for catalytic conditions (Figure 4) provides some information about the mechanism for formate formation with either H 2 O or AnsdH + and how those mechanisms may differ slightly as a function of the proton source. As described earlier, under reaction conditions with low [H + ], there is an anodic shift in E p,c (1 3−/4− ) due to the folfast PT reaction which affords (H-1) 3− from 1 4− . The anodic shift in E p,c (1 3−/4− ) from E 1/2 is 140 and 100 mV with H 2 O or AnsdH + , respectively, under 1 atm CO 2 ( Table 1). As the [H + ] increases, the catalytic current response with H 2 O gradually shifts cathodically, whereas the response under AnsdH + remains at E cat/2 = −0.78 V ( Table 2). Both of these behaviors are common in molecular electrocatalysis and indicate nuances in the reaction mechanism. With AnsdH + , the constant value of E cat/2 over a wide range for [H + ] simply suggests that the mechanism for formate formation (or background H 2 evolution) is unchanged even as the concentration of (H-1) 3− available in solution increases with increased [H + ] (Scheme 2). When H 2 O/ carbonic acid is the proton source, then at higher [H + ], E cat/2 for 1 2− shifts cathodically so that E cat/2 ∼ E 1/2 at [H + ] max . Water (or carbonic acid) is a weaker acid than AnsdH + by 5 pK a units. The cathodic shift in E cat/2 with increased [H + ] may therefore arise from a competing bimolecular evolution of H 2 as has been described in prior reports by us 31 and by others (Scheme 1). 48 It is also possible that more negative potentials are needed to drive hydride transfer from (H-1) 3 (Table S1).
(k 1 ) (vide supra). Therefore, the formation of (H-1) 3− can be considered as a pre-equilibrium step with both a forward and reverse rate constant, k 1 and k −1 , and an equilibrium constant, A key feature of the pre-equilibrium mechanism is that k obs is enhanced linearly according to the magnitude of K 1 : that is a "normal" mechanism would have k obs = k 2 [CO 2 ], but the pre-equilibrium mechanism has k obs = K 1 k 2 [CO 2 ] (eq 1, and the terms and units were defined earlier). Even at very low ratios of [H + ]/[1 2− ] under 1 atm CO 2 , the 1 3−/4− redox couple is irreversible, and therefore, we cannot determine K 1 using an electrochemical measurement (Figure 3 right). 49 However, we can estimate a value for K 1 if we know the pK a value for (H-1) 3− and the pK a values for the proton sources used for catalysis, which are CO 2 saturated H 2 O and AnsdH + . We determined the pK a value for (H-1) 3− as 24.6 using infra-red spectroelectrochemical titrations of 1 4− with acid sources (Calculation S5, Figure S9). We then used thermochemical cycles to determine the values for K 1 from the pK a values of (H-1) 3− , CO 2 saturated water, and AnsdH + (Calculation S3). The values of K 1 were determined as 15.8 and 5.5 × 10 12 , when CO 2 saturated water or AnsdH + are used as the proton source, respectively. 50−52 Using the experimentally determined value for k 1 , this calculation further provides an estimate of k −1 as 1.2 × 10 4 and 5.4 × 10 −5 M −1 s −1 , when CO 2 saturated water or AnsdH + are used as the proton source, respectively, since K 1 = k 1 /k −1 . According to these estimates, K 1 > 1, and we should expect that the preequilibrium formation of (H-1) 3− enhances k obs relative to k 2 (eq 1, Scheme 2).
Catalyst Benchmarking. As mentioned in the introduction, we predicted that two features of the catalyst performance (rate and overpotential) will be enhanced by the preequilibrium reaction kinetics, relative to reports of formate formation by other molecular catalysts. These two effects are nicely illustrated using a Tafel style plot where the TOF (which is equivalent to k obs above) is plotted as log 10 (TOF/ s −1 ) versus overpotential (V). On this plot, formate formation by 1 3− is illustrated using both AnsdH + and H 2 O as the source of protons ( Figure 5). Overpotential is defined as where η is overpotential (mV), E COd 2 is the thermodynamic potential for reduction of CO 2 into formate under standard conditions (mV), and E cat/2 is the potential at which the catalytic current density reaches half of its maximum current (i cat/2 and see Calculation S1). 53 Kinetic enhancements to k 1 result in a low overpotential for the catalytic reaction at 64 mV using 1 3− in MeCN/AnsdH + . Specifically, E 1/2 for 1 3− is −0.95 V, but E cat/2 is −0.78 V, and the 170 mV anodic shift in E cat/2 has a kinetic origin in the extremely fast PT rate and formation of (H-1) 3− , at 3 × 10 8 M −1 s −1 . Another example of a very fast formate forming catalyst is [(bipy)Co(PyS) 2 ] + which has TOF similar to 1 3− while the overpotential remains pinned to the value of E 1/2 so that the overpotential for formate formation is 110 mV. 54 A plot of Log 10 (TOF/s −1 ) versus E cat/2 for molecular catalysis of CO 2 to formate shows a linear correlation ( Figure  6). Absent kinetic effects, a linear free-energy relationship (LFER) should exist between Log(TOF/s −1 ) and hydricity (free energy for loss of hydride, ΔG H − ) over a series of catalysts. 55 It is also known that ΔG H − scales roughly with E cat/2 and pK a of the catalytic hydride intermediate over a series of catalysts having similar mechanism, and this relationship underlies a rough correlation between Log 10 (TOF/s −1 ) and E cat/2 . Given that the structure of 1 3− is different than the structure of the single-site metal catalysts that comprise most of the catalysts in Figures 5 and 6, it is possible that 1 3− does not fall on the ΔG H − versus E cat/2 correlation line for those compounds. Therefore, we include a brief discussion using ΔG H − as a benchmark against related catalysts to complement the observations in Figure 6.
Catalyst Design for a Pre-Equilibrium Mechanism. These findings illustrate how clusters, or more generally nanosized materials with delocalized electronic structure, can be employed to enhance the reaction rate of the first chemical step in the catalytic cycle to achieve the pre-equilibrium mechanism. The active catalyst, 1 3− , has 3-charge while retaining a very modest reduction potential of −0.95 V. The low potential, despite the high anionic molecular charge, likely arises from low reorganization energy associated with the delocalized bonding in the metal−metal bonded cluster; the fast PT to afford (H-1) 3− may be promoted by the high anionic charge on intermediate 1 4− , by the large array of almost-identical surface sites that are available to react with the proton, and by a low reorganization energy for the PT. In any electrochemically driven catalytic cycle, a fast chemical step following ET will lower the overpotential for catalysis, as defined in eq 3, since E cat/2 is kinetically shifted by the fast chemical step.
Using the cluster structure to achieve a pre-equilibrium mechanism has further advantages beyond the lowered overpotential described in the preceding paragraph. Following generation of the intermediate, in this case (H-1) 3− , there is now just one reactive site on the catalytic intermediate, and thus, the selectivity of the second chemical step remains under thermochemical control with a rate that is enhanced by the pre-equilibrium value of K 1 according to eq 1.
Regarding f uture applications of the pre-equilibrium mechanism to enhance the electrocatalyst performance, there are a few obvious scenarios that come to mind. The establishment of the pre-equilibrium depends on the reactivity of both the catalyst (more precisely, the catalyst following a redox event) and the substrate that is required for intermediate formation.
These will be discussed separately. Regarding the catalyst: heterogeneous and nano-scale catalysts possess delocalized structures and multiple reactive surface sites similar to the clusters described herein and should be amenable to design of pre-equilibrium mechanisms for solar fuel chemistry. Molecular catalysts, likewise, are promising candidates, and proton relays are a structure type in this category that is well-known to be effective in fast and low overpotential H2 evolution from protons. Beyond, proton reduction, new strategies in molecular chemistry must provide multiple sites for specific substrate binding or site specificity, and possible ideas in this area include incorporation of H-bond accepting or -donating functional groups that are chosen with a pK a value that is not suitable for proton relay behavior. A nucleophilic molecular catalyst is another obvious approach, but that is not a good one since it also results in high energy (very cathodic potentials in the case of reduction) for the catalytic turnover.
Regarding the substrate: in this work, the substrate needed for intermediate formation was a proton, and the proton activity is easily changed (and benchmarked according to the pK a scale) to promote a large equilibrium constant (K 1 : see eq 1, Scheme 2). The tuning of substrates such as CO 2 , CO, or N 2 may be a little more challenging, but strategies are known which can drive fast catalyst/substrate interactions that have high equilibrium constants. As examples, Lewis acid cocatalysts are known to polarize overall non-polar molecules including N 2 and CO 2 , just like the anion associated with a proton changes its pK a value and activity. Other mechanisms for tuning the reactivity of substrates include use of heterogeneous or homogeneous electrocatalysts with chemically inequivalent bind sites to polarize incoming substrates, to serve as ET sites, and to stabilize intermediates and enhance K 1 .
It is apparent from the foregoing discussion that many of the catalyst design strategies reported by researchers in the heterogeneous and homogeneous electrocatalysis and solar fuel communities may already be drawing on pre-equilibrium reaction mechanisms to achieve high performance through tuning of the catalyst, substrate, or both. Recognition of those pre-equilibrium mechanisms will result in better control and further enhanced performance because it can guide tuning of elementary steps in the catalytic cycles. Alternatively, minor adjustments to the substrate choice or catalyst design may induce pre-equilibrium mechanisms from existing catalytic cycles that involve successive ET and chemical reaction steps.

■ CONCLUSIONS
In this report, we described a general strategy for use of the pre-equilibrium reaction mechanism to enhance the reaction rate. This was illustrated for formate formation from CO 2 and catalyzed by [Co 11 C 2 (CO) 23 ] 3− (1 3− ). Relative to the known LFER for Log 10 (TOF/s −1 ) versus E cat/2 for reported catalysts, the reaction rate to form formate was enhanced by 5 orders of magnitude, and the overpotential was lowered by 100 mV. Specific to the example demonstrated herein, pre-equilibrium metal-hydride formation led to the enhanced catalyst performance. Selectivity for formate formation (over H 2 formation or other CO 2 reduction products) arises from the thermoneutral hydride transfer elementary chemical step, whereas preequilibrium kinetic effects originate in the hydride formation at 3 × 10 8 M −1 s −1 . A rationale for the observed rates and selectivity were discussed in this report, in relation to the nanoscale structure of 1 3− and the choice of the proton source which both promote the pre-equilibrium reaction mechanism. In addition, the generality and clearly understood origin of the effects presented herein can be applied broadly to the design of homogeneous and heterogeneous catalysts, and possible strategies to achieve this in future efforts were discussed. ■ ASSOCIATED CONTENT * sı Supporting Information